Public Domain are ours to use freely as part of the inheritance of all the world, free from royalties. In practice it means that the Copyright has lapsed and the Trademark might still be in force, or legally contestable. Things pass into the Public Domain most often through sheer neglect. But once anyone smells the possibility of making money off of something, they tend to get interested real quick. One good case in point is the use of the long forgotten 1940's characters from the Nedor Comics characters in Tom Strong by Alan Moore and the subsequent invention by Moore of Terra Obscura which placed Public Domain characters into the peculiar position of being re-copyrighted and trademarked by ABC, which was part of Wildstorm and then DC. An explanation of the intricacies involved in this situation can be had from the Newsarama archives on the Nedor Heroes being the property of DC/ABC/Everyone. This was truly a most fascinating chain of events.
Usually, Public Domain is a fairly safe thing to mine for free stuff. But in terms of Comics and Pulp Heroes and Villains...it gets a bit trickier than just reviving an obscure character. Trickier, but eminently do-able, if you do the research involved in due dilligence. If these sorts of characters/opportunities appeal to you, then you might consider reading through Ivan Hoffman's various articles including the one on The Protection of Fictional Characters. And there are a LOT of these old, neglected characters out there for anyone wanting to go and seek them out.
Some defunct Comics Publishers such as Fox Feature Syndicate, Crestwood Publications, Quality Comics, Spark Publications, and others have left behind an massive collection of characters that have barely been tapped-into by a few intrepid explorers of the Public Domain such as Alan Moore, though tehre are a few new publishers really making a concerted effort to mine this treasure such as AC Comics who provide a very interesting series of Golden Age Reprints and an "Official" Golden Age Heros & Heroines Directory, and Moonstone Books which are in the process of reviving Karl Kolchak (Darren McGavin Rocks!), Buckaroo Banzai, The Green Hornet and a host of other Characters and franchises including such Public Domain characters you know and love or might never have heard of before such as Sherlock Holmes, Mandrake the Magician and many, many others (even The Spider!). Moonstone is bringing back a lot of Original Characters from the brink of the abyss, and they are bring out comics based on The Saint, Captain Action, Mister Moto, The Avenger, and other classics as well as reviving the old White Wolf fiction, which is ...odd... but as a publisher mining the old and obscure, Moonstone are definitely worth checking out.
You can find a bit more information, including thumbnail pictures in most cases, about Standard/Better/Nedor Comics' Characters, Fox Features Syndicate Characters, Quality Comics Characters, and Spark Publications Characters (and piles more!) over at the International Catalogue of Superheroes (an essential resource for researching all sorts of old, forgotten, lost or abandoned Pulp and Comics characters irregardless of their being in the Public Domain or not: a truly wonderful resource is the page dedicated to Various Golden Age Characters where you can look-up some really obscure publishers like Centaur and others).
Jeff Rovin has also published a pretty comprehensive Encyclopedia of Superheroes, as well as an Encyclopedia of Monsters, both of which might be of interest or use in researching the old, out-of-date and Trademark-expired Heroes and Villains of Yesterday. You can find a lot of old names, publishers and stuff to start your own search. Another online resource to consider is the Golden Age Comic Book Stories blog where you could easily loose hours digging through some amazing and fun stuff. The Digital Comics Museum and you can view a nice gallery of Golden Age comics covers at the excellent Ben Samuels Design webite as well (That's where we found the nifty Black Terror cover used above).
If your tastes run a bit more to the European end of the Comics spectrum, you can check out Lambiek and their Comiclopedia, Cool French Comics, or Black Coat Press and their comic imprint: Hexagon Comics. There are dozens upon dozens (hundreds?) of European (not just French!) Heroes and Villains languishing in obscurity, some of whom are in the Public Domain, others who are just waiting to be revived by an interested writer/artist and translator.
There are also a couple of online Comic Database projects like Comicbookdb, (They have a Blog as well) and the Grand Comics Database (Wiki), both of which seem to be doing more or less the same task, cataloging every last scrap of information that they can gather on any and every comic ever produced. There's a lot of information at those two sites/projects, and you can volunteer to help out as well. If you have any spare time on your hands. If you're so inclined.
Public Domain Super Heroes (Wikia) is an incredible resource. As is Project Rooftop and especially their Retro-Fix column where an artist will re-imagine/re-design the look of an older, public domain character. Very inspirng, especially the recent redesign of Zardi: The Eternal Man, which really looks cool. It's similar to the Comic Twart Blog, only for Public Domain characters.
Whew. That's a lot of stuff. But it's far from exhaustive. You can get a pretty good start on digging around for old timey Pulp and Golden Age goodness from here though.
Huh. I would have thought that would be obvious. There's a ton of stories, characters and loads of art out there that we can learn from, if only to use as a source of inspiration and self-education. Tarzan is cool, but once you look over some of the alternatives, parallels, and blatant rip-offs, you start to see some fairly archetypal themes and a host of fresh insights start to bubble up from the depths of the primordial collective unconscious. Wandering barbarians are a dime-a-dozen, but when you familiarize yourself with a dozen or more such characters, you really get a feel for the plots and stories that have been done to death, the tried-and-true, the boring cliches and a peculiar, divine dissatisfaction comes over you --or you cave-in to ennui and waddle off on another tangent-- and you begin to see ways that things could have been or should have been or might have been different. And then you start to write, draw or create and you either breathe life back into some forgotten character, or you create and contribute your own brand new hero or villain to the overall mix.
Why endlessly repeat and regurgitate the stuff of the past when we can use it as a hyper-fertile matrix for growing fresh new stuff? Reviving old heroes was old when the Greeks were doing it. It was stale when Sinbad did it. And yet those stories are as timeless as they are shameless, and we keep on re-tooling them, re-editing them, and re-presenting them, only now this time in a blue cape or with a domino mask and a pair of hand guns...
The Public Domain is all our tool-set and playing field combined. Those characters relegated to it are ours to use as we see fit, so long as we do our research and are clear on what all someone else has already done or is currently doing, and we take steps to make it uniquely our own interpretation. Like how Kevin Smith is reviving The Green Hornet for Dynamite as opposed to the stuff coming out via Moonstone. They're also doing their own version of Zorro and a few others. I guess it comes down to "Let the best writer/artist team win." Kind of like capitalist publishing gladitorial combat.
It's nice to have choices. Not every superhero belongs in the modern age, or even in a retro-steampunk/dieselpunk setting. Some heroes translate exceptionally well to the prevailing conventions of Fantasy, dark or otherwise. Zorro is amazingly easy to re-adapt to a faux-medieval setting, just as Robin Hood morphed into DC's Green Arrow fairly easily. The Shadow could just as easily wield twin hand-crossbows as .45s, and The Spider would make for an intimidating character in just about any setting you cared to bring him into. Doc Savage would be a worthy replacement for Merlin in King Arthur's court, just as he could easily take Gandalf's place...and probably change the flow of things so drastically that you'd have an entirely new story that'd be both exciting and very, very different than a band of pedestrians taking forever to deal with the world-threatening crisis.
Exceptional characters are fun, when handled appropriately. Sure, they can easily dominate or wreck a typical world that is not ready for them, but given some thought and consideration, you can adapt Pulp hereoes and Golden age superheroes--and villains--into your setting, making suitable modifications so that Fu Manchu becomes Ambassador DeCluny, or some C-list gunslinger is transformed into a masked bandit stirring up trouble in the Eastern Forests, or that freakish meteorite that recently streaked across the midnight sky has birthed a whole generation of peculiar mutant offspring similar to Philip Jose Farmer's Wold Newton Family. And that's without introducing aliens, ghosts or time travllers...
The sky was never the limit.